Currently you'll need to install Mozilla. I want to make it work with Firefox like Gtk2::MozEmbed does, but I have to test it (which requires me actually installing Firefox). Mozilla will install libraries:
You'll want at least version 1.7.5 of Mozilla, since that's what I used, though it might work with earlier versions.
Mozilla::DOM will not work with Windows. In order to get it to work with Windows you'd have to make ExtUtils::Depends work with Windows, which I'm not sure that it does. I don't use Windows. Mozilla::DOM may work on MacOS X, but nobody has confirmed that. I don't use MacOS X.
You can't currently use Mozilla::DOM without showing a window, as far as I know. It might be possible to create a kind of "null" widget toolkit library, equivalent to Gtk, Qt, or wxWidgets, that doesn't require displaying windows; then wrap it in Perl and use it in the same way that you use Gtk2::MozEmbed.